OTTAWA — The Canadian health-care system has proven to be a black hole for federal tax dollars over the past decade or so, says a new report.

Despite hikes in federal transfers to provinces for health care that were $97.6-billion beyond what was needed to account for inflation and population growth in the past 13 years, there has been little improvement in access to care for Canadians, says the Fraser Institute study released Wednesday.

As an example, the report noted the time it takes to get treatment from a specialist after a referral from a general physician. The median time was 19 weeks last year, up almost 60% from 1997.

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“Canadians should have expected the health-care system to improve, and it’s troubling that there has not been an improvement in spite of this very large increase in health-care expenditures since 1997-98,” said Nadeem Esmail, a senior fellow at the Fraser Institute and co-author of the study.

He said the Canada Health Act is constraining provinces from improving the efficiency of their systems. Allowing people to pay for quicker access to care, and more private-sector involvement in health insurance and delivery, while still ensuring universal access for all, are among the measures Mr. Esmail recommends.

“The core problem here is that the Canadian health-care system is relying on an inefficient model for health-care policy, that is we have a preponderance of government in the health-care system,” Mr. Esmail said. “Government is delivering health care and government is regulating health care.”

The report found that since 1997 wait times have increased for getting an appointment with a specialist after a referral, getting treatment from a specialist after the initial consultation, getting a CT scan and getting an ultrasound. It also found fewer nurses in proportion to the population, as well less availability of lithotripters (machines that break up kidney stones so they can be more easily passed).

The study did find improvements in four of the 11 factors it compared between 2011 and 1997; there were more physicians, MRI machines and CT scanners per capita, as well as shorter wait times to get an MRI.

However, Mr. Esmail said it’s a sign of the system’s general inefficiency that wait times for a CT scan increased despite greater availability of the equipment. He also noted that the number of available MRI machines increased 353.8% in proportion to the population, but wait times to use them fell by just 4.2%.

He said he is not suggesting a move toward U.S.-style health care, but something closer to the models in Switzerland, France and Japan. Those countries allow more private-sector involvement in universally accessible health-care systems and have produced better results than Canada has.

The Fraser Institute’s study did not specifically look at health-care outcomes, and Mr. Esmail acknowledged at least some of the increased funding seen in Canada in recent years has improved the quality of patients’ health after treatment.

“The reality is that it would be very difficult to spend $97.6-billion without buying something,” he said.

On how much of the money went toward serving an aging population, Mr. Esmail said this accounts for just one percentage point of the 6.9% average increase in annual health-care costs since 1997.